If the eigenvalue of matrix A is t, why is the eigenvalue of K power of a K power of T,

If the eigenvalue of matrix A is t, why is the eigenvalue of K power of a K power of T,

AA = Xa, X is the eigenvalue of A
A ^ Ka = a * a * a *. A (k a) a = a * a * a *. A (k-1 a) AA = a ^ (k-1) AA = a ^ (k-1) XA = a ^ (K-2) XXA =
=x^ka
So we have to prove it

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